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# Title: Où il répond à plusieurs difficultez qui luy ont esté proposées sur la Dioptrique, la Geometrie, & sur plusieurs autres sujets (shelfmark Leibn. Marg. 43:3)
# Folio 479, page id 82327652X:0507
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=82327652X&page=507
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.79
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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11
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9IV
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DE NI DESCARTES.
Iysiminuenio ~ p Y= X X
F cxX = = b r r ex qua aqua-
D X X
tione facile habetur punctum B per meam Creometriam;
NTam (i a e c sincxquales, sumenda est cantum in axe Y R,
quae siemedia pars dara FL, ec perpendicularis RS, qua
SiE media pars datae F F, ductusque circuluS ex CeNFrO S
per verricem sectionis CF, Secabic parabolam in guae sieo
puncto B; Si aurem a e cnon sineaquales, paulo quidem
prolixior erichac constructio, sed non difficilior. Invenco
aurem puncto B, duco rectam A B, itemque AL ip(IX qua-
lem, ac parallelam axi C Y, estque B L una exdiamerris
ellipseos quasiex, atque linea per eius cenerum D ducta,
perpendicularis linex a D, ac parallela plano sectionis, in
conici superficie verimque cerminata, elc alia diameter
Priori conjusata.
Instieuitur aurem Analysis ad punctum B inveniendum
hoc pacto. Ex daris X a TumpEIS AC, EF, FL, YG, GN
ec NV. B quaeritur a B, icemque B P, cansens parabolam in
B, e facta BII aquali ip(i A B, X axi C Y parallela, inve-
BIEUT AH, Cx A 9, OB e B FI; iremque FI R parallela
tansenti B P; Tremque H M perpendicularis a puncto a
in axem C Y; TLCMqUC M C7 X MI Y; acque ex daris vel
aTumpeiS A C, F F, FY, M Y _ R M, invenitur A K
cuius quadrarum aequari debet quadraris ex L H _C A H;
quia ve angulus a D B, ita eriam a e k rectus eAt. ACque
aequario quae per hanc riam invenieur est hXC
X II X x t CY X = = brY
Fadem plane ratione instiruerur Analysis in hyperbola,
e in ellips; e quamuis aliquanto incricarior ec longior sie
fucura, nececsario camen reduci porerie ad aequarionem.
quae quaruor dimentiones non excedee, aequeidcircoiuxra
meam Creomerriam, per solam regulam ee circinum, in
data conica sectione construerur.